JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
    If one end of a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y+11=0\]be (3, 4), then the other end is [MP PET 1986; BIT  Ranchi 1991]

    A)            (0, 0)                                         

    B)            (1, 1)

    C)            (1, 2)                                         

    D)            (2, 1)

    Correct Answer: C

    Solution :

               Centre is (2, 3). One end is (3, 4).                    \[{{P}_{2}}\] divides the join of \[{{P}_{1}}\] and O in ratio of 2 : 1.                    Hence \[{{P}_{2}}\] is \[\left( \frac{4-3}{2-1},\ \frac{6-4}{2-1} \right)\equiv (1,\ 2)\].


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